# Linear Equations in Real Life by JohnQuinn

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```									        Real World
Applications of
Linear Equations
Yes, there really are uses for them!!

Math 208 ~ College Mathematics I
Objective: Apply the concepts of slope and intercept to real-life situations
Today’s Objectives
 To define the slope of a
linear equation a real world
context
 To find a meaning for an

equation’s x & y-intercepts
Brief Review of Graphing
   Solve the equation for y        2x + y = 3

y = – 2x + 3
   Make a table and find       x   y = –2x + 3     y
–1
some ordered pair                y=2+3          5
0    Y=0+3          3
values                      1   Y = –2 + 3      1
2   Y = –4 + 3     –1
Graph the Equation
   Graph the ordered
pairs
(-1, 5)
   Draw the line            (0, 3)
(1, 1)
(shows all the              (2, -1)

possible solutions)
First Problem to follow along.
Use the handout

What do we know?
 A pillow company buys ribbon in 100 foot
rolls.
 2.5 feet of ribbon are needed to decorate
each pillow.
What do we need to do?
 Write an equation. Use y for the amount
ribbon left on the roll and x for the number
 Fill in the table and draw the a graph.
Write Equation & Fill in the Table

# Pillows                    # of Feet of Ribbon
Made      y = 100 – 2.5x   Remaining on Roll

0          100 – 0               100
1          100 – 2.5              97.5
2          100 – 5                95
3          100 – 7.5              92.5
4          100 – 10                90
Draw the graph
100
90
80
70
60
50
40
30
20
10

1   2   3   4 5   6   7   8   9 10
Questions for
100

90

80

Discussion
70

60

50

40

30
y = 100 – 2.5x
20

1. What is the slope?
10

1   2    3   4 5   6   7   8   9 10

What does it represent?
2. Why is the slope negative?
3. What is the y-intercept? What does
it represent?
4. What is the x-intercept? What does
it represent?
Second Problem
What do we know?
 A swimming pool holds 450 gallons of water.

 The pool currently contains 100 gallons of
water.
 A hose deposits 50 gallons of water in the
pool each minute.
What do we need to do?
 Write an equation. Use y for the amount of
water in the pool and x for the number of
minutes the hose runs.
 Fill in the table and graph the information.
Fill in the Table

# of Minutes Hose                   # of Liters in
is in Pool     y = 100 + 50x     The Pool

0            100 + 0             100
1            100 + 50            150
2            100 + 100           200
3            100 + 150           250
4            100 + 200           300
Draw the Graph
500
450
400
350
300
250
200
150
100
50

1   2   3   4 5   6   7   8   9 10
500

450

Questions for     400

350

Discussion
300

250

200

150
y = 100 + 50x
100

1. What is the slope?
50

1   2   3   4 5   6   7   8   9 10

2. What does it represent?
3. What is the y-intercept? What
does it represent?
4. Why does this graph contain a
line segment (have an end)?
Conclusions
   What kinds of real life applications are linear?
(What do these situations have in common?)
They both have a Constant Rate of Change (SLOPE)
   What does the slope represent?
The slope represents the rate of change

   What does the y=intercept represent?
The y-intercept represents the y value before the
rate begins. x = 0

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